The private broadcast fuzz test does not use any randomness.
This was added in #35129 based on a draft created in #29415. That draft was created when the state of #29415 was still using SaltedTxidHashers, but this usage was removed before it was merged.
Setting the random state while not using it is causing issues with nightly https://github.com/maflcko/bitcoin-core-nightly/issues/25.